Evaluate fourth root of 243

Problem

√(4,243)

Solution

1. Identify the number under the radical and look for its prime factorization.

2. Factor the number 243 by dividing by 3 repeatedly.

243=3⋅81

243=3⋅3⋅27

243=3⋅3⋅3⋅9

243=3⋅3⋅3⋅3⋅3

243=3

3. Rewrite the expression using the prime factorization.

√(4,3)

4. Simplify the radical by pulling out terms that are powers of 4.

√(4,3⋅3)

5. Apply the property of radicals √(n,a⋅b)=√(n,a)⋅√(n,b)

√(4,3)⋅√(4,3)

3⋅√(4,3)

Final Answer

√(4,243)=3√(4,3)

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